User hrkrshnn

36 votes

Best Fake Proofs? (A M.SE April Fools Day collection)

answered Apr 1, 2013 at 16:53

32 votes

What are some conceptualizations that work in mathematics but are not strictly true?

answered Jul 24, 2014 at 14:18

31 votes

Accepted

How to solve this sequence $165,195,255,285,345,x$

answered Jun 3, 2014 at 15:39

17 votes

Accepted

Problem 6 - IMO 1985

answered Jul 4, 2014 at 16:05

17 votes

How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?

answered Mar 30, 2014 at 5:08

14 votes

Prove that ${1\over2}<{1\over1001}+......+{1\over2000}<1$

answered Jun 6, 2014 at 11:41

14 votes

Interview riddle

answered Jul 15, 2014 at 9:35

13 votes

Accepted

If $f$ is a strictly increasing function with $f(f(x))=x^2+2$, then $f(3)=?$

answered Jun 13, 2014 at 12:00

12 votes

what is the one point compactification of R?

answered Jun 16, 2016 at 18:50

11 votes

Accepted

What are some difficult integrals done by substitution and elementary functions?

answered May 9, 2013 at 15:10

10 votes

Prove that a continuous image of a closed subset of a compact space is a closed subset

answered Nov 5, 2015 at 8:32

10 votes

Accepted

Prove that there exist $a \in [-1,1]$, such that $f'''(a)=3f(1)-3f(-1)-6f'(0)$

answered Aug 28, 2014 at 13:46

10 votes

Accepted

For continuous functions, preimage of open set is open.

answered Sep 6, 2014 at 8:59

8 votes

Accepted

Prove that $\sum\limits_{n=0}^{\infty}{(e^{b_n}-1)}$ converges, given that $\sum\limits_{n=0}^{\infty}{b_n}$ converges absolutely.

answered Jul 2, 2014 at 8:51

7 votes

Accepted

Prove that $2^{4n}+1$ cannot be a prime if $3|n$

answered Mar 18, 2015 at 11:45

7 votes

Evaluate a limit (probably involving L'Hôpital rule)

answered Jun 3, 2014 at 15:04

7 votes

Prove the absolute value function of a continuous function is continuous

answered Jul 15, 2014 at 13:22

7 votes

Accepted

A question about limits at infinity

answered Mar 27, 2014 at 12:39

6 votes

Accepted

Is it possible to solve for two unknowns from one equation?

answered Mar 30, 2013 at 17:36

6 votes

Accepted

Find $\lim_{n\to\infty}2^n\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt2}}}}_{n \textrm{ square roots}}$.

answered Jun 24, 2013 at 7:49

6 votes

Is $M=\{\frac{1}{k}|k \in \mathbb{N}\}$ closed?

answered Jun 16, 2014 at 10:09

5 votes

Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$

answered Jul 2, 2014 at 6:07

5 votes

Accepted

Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$

answered Aug 11, 2014 at 12:18

5 votes

Does This Sequence Converge or Diverge?

answered Feb 23, 2014 at 16:42

5 votes

Accepted

Find a polynomial as $2836x^2-12724x+16129$

answered Mar 22, 2013 at 17:01

5 votes

Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?

answered Mar 22, 2013 at 15:04

5 votes

Prove that $\limsup _{n\to \infty}(a_n+b_n)\leq \limsup _{n\to \infty}a_n + \limsup _{n\to \infty}b_n$

answered Jul 1, 2014 at 13:28

5 votes

Accepted

A circular proof in Rudin that $\mathbb{R}$ is a field.

answered May 25, 2014 at 15:13

5 votes

What is the highest $n$ such that $15^n\mid 100!\;?$

answered Jun 1, 2014 at 16:54

4 votes

Accepted

The product of a uniformly continuous function and a bounded continuous function is uniformly continuous

answered Jul 15, 2014 at 17:04

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125 Answers

Best Fake Proofs? (A M.SE April Fools Day collection)

What are some conceptualizations that work in mathematics but are not strictly true?

How to solve this sequence $165,195,255,285,345,x$

Problem 6 - IMO 1985

How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?

Prove that ${1\over2}<{1\over1001}+......+{1\over2000}<1$

Interview riddle

If $f$ is a strictly increasing function with $f(f(x))=x^2+2$, then $f(3)=?$

what is the one point compactification of R?

What are some difficult integrals done by substitution and elementary functions?

Prove that a continuous image of a closed subset of a compact space is a closed subset

Prove that there exist $a \in [-1,1]$, such that $f'''(a)=3f(1)-3f(-1)-6f'(0)$

For continuous functions, preimage of open set is open.

Prove that $\sum\limits_{n=0}^{\infty}{(e^{b_n}-1)}$ converges, given that $\sum\limits_{n=0}^{\infty}{b_n}$ converges absolutely.

Prove that $2^{4n}+1$ cannot be a prime if $3|n$

Evaluate a limit (probably involving L'Hôpital rule)

Prove the absolute value function of a continuous function is continuous

A question about limits at infinity

Is it possible to solve for two unknowns from one equation?

Find $\lim_{n\to\infty}2^n\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt2}}}}_{n \textrm{ square roots}}$.

Is $M=\{\frac{1}{k}|k \in \mathbb{N}\}$ closed?

Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$

Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$

Does This Sequence Converge or Diverge?

Find a polynomial as $2836x^2-12724x+16129$

Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?

Prove that $\limsup _{n\to \infty}(a_n+b_n)\leq \limsup _{n\to \infty}a_n + \limsup _{n\to \infty}b_n$

A circular proof in Rudin that $\mathbb{R}$ is a field.

What is the highest $n$ such that $15^n\mid 100!\;?$

The product of a uniformly continuous function and a bounded continuous function is uniformly continuous